This invention relates generally to polyphase code systems and more particularly to digital systems for decoding sequences of polyphase encoded signals.
In a conventional radar, the transmitted waveform is a train of pulses as shown in FIG. 1a of the accompanying drawing. The average power is determined by the peak power and the duty ratio, that is to say the ratio of the width of the pulses to the overall repetition period T. T is generally fixed by the maximum unambiguous range, and .tau. by the resolution required. Thus, to improve the detectability of the radar only the peak power can be increased and this is limited by the components used. There is therefore a conflict of interests if both improved detectability and resolution are required.
It is now recognized that the resolution is not governed by the pulse length but by the overall transmitted bandwidth. Thus, by modulating the carrier within the transmitted pulse length the bandwidth is increased and the resolution improved with no reduction in average transmitted power.
One known form of modulation to effect pulse compression is phase modulation in which, within the width of the transmitted pulse, the phase is changed at specified intervals or subpulses. While these phase changes can follow a random sequence, by using certain well-defined sequences known as "Frank codes" it is possible to reduce the level of the sidelobes after processing of the received pulse. An example of a known method to transmit and detect Frank-coded radar pulses is described in U.S. Pat. No. 4,237,461.
In FIG. 1(b) of the drawing, there is shown the pattern of phase changes within a pulse 11 subdivided into an even number (4) of subsequences of subpulses, 11a-d, each subsequence having four subpulses, .tau. seconds long, so forming a Frank code with a pulse compression ratio of (4).sup.2 =16. The subpulses are at a constant carrier frequency and related to a CW reference signal by a phase angle of (n)(90.degree.), where 0.ltoreq.n.ltoreq.3. The phase, in radians, encoded on each of the subpulses 11a-d of the pulse 11 may be determined from the matrix of Table 1, as read from left to right progressing from the top to the bottom row.
TABLE 1 ______________________________________ 0 0 0 0 0 .pi./2 .pi. 3 .pi./2 0 .pi. 0 .pi. 0 3 .pi./2 .pi. .pi./2 ______________________________________
A counterclockwise phase rotation (phase advance) has arbitrarily been assigned a positive value while a clockwise rotation (phase delay) is assigned a negative value. A phase advance of X radians is equivalent to a phase delay of 2.pi.-X radians.
The subpulses can be represented by phasors, i.e. defined as vectors in a coordinate system rotating at the carrier frequency of the transmitted pulse. The length of the vector represents the magnitude of the subpulse; its angle with the x axis represents its phase relative to the carrier. The component of the vector along the x axis is in phase with the carrier; the component of the vector along the y axis is 90 degrees out-of-phase with the carrier. If the x axis is designated the real axis and the y axis is designated the imaginary axis, the phase in complex numbers is shown in Table 2. (Note that positive angles are measured in the counterclockwise direction and an advance of phase is represented by a counterclockwise rotation. Thus, a phase shift of .pi./2 is +J in complex numbers and a phase shift of -.pi./2 is -j in complex numbers).
TABLE 2 ______________________________________ 1 1 1 1 1 +j -1 -j 1 -1 1 -1 1 -j -1 +j ______________________________________
The phases encoded on the four subpulses of the first subsequence 11a are indicated in the top row of the matrix of Table 1 or Table 2; the phases encoded on the four subpulses of the second subsequence 11b are indicated in the second row of the matrix; the phases for the four subpulses of the third subsequence 11c in the third row; and the phases for the four subpulses of the fourth subsequence 11d in the fourth row. Examining the phases encoded on the four subpulses of each subsequence 11a-d, it will be seen that the phase increases linearly from subpulse to subpulse at a rate of 0 radians per subpulse in the first subsequence 11a; at a rate of .pi./2 radians per subpulse in the second subsequence 11b; at a rate of .pi. radians per subpulse in the third subsequence 11c; and at a rate of 3.pi./2 (or-.pi./2) radians per subpulse in the fourth subsequence 11d. Examining the slope of the phase increase of each subsequence, it will be seen that the slope increases linearly from subsequence to subsequence at a rate of .pi./2 radians per subsequence. Since frequency is the rate of change of phase, linearly increasing phase is a constant frequency. This, each subsequence 11a-d represents a different frequency measured with respect to the carrier frequency, viz. 0, (.pi./2)/.tau., .pi./.tau., and (3.pi./2)/.tau. or (-.pi./2)/.tau. respectively for each of the subsequences in order. Since the frequency (slope of phase) also changes linearly by (.pi./2)/.tau. from subsequence to subsequence, the Frank code is seen to be a step-wise approximation to a swept frequency.
The amplitude of the auto-correlation function of pulse 11 as might be obtained after the matched filter of a pulse-compression radar receiver is shown in FIG. 1c. This graph shows the level of correlation of a pulse as in FIG. 1b with a similar pulse when plotted against the relative time of the pulses being completed. It will be seen that except at coincidence in time, the correlation function takes on values between 0 and .sqroot.2 and that when the two signals are coincident the correlation function has a value of 16. This means that though the transmitted pulse has an overall duration of 16.tau., the resolution of the radar is 1 .tau. and there is a ratio of 16 to .sqroot.2 between the correlation peak and the peak sidelobes.
FIG. 1d of the drawing shows the pattern of phase changes within a pulse 12 subdivided into an odd number (3) of subsequences of subpulses, 12a-c, each subsequence having three subpulses, .tau. seconds long, so forming a Frank code with a pulse compression ratio of (3).sup.2 =9. The subpulses are at a constant carrier frequency and are related to a CW reference signal by a phase angle of n (120.degree.), where 0.ltoreq.n.ltoreq.2. The phase in radians, encoded on each of the subpulses 12a-c of the pulse 12 may be determined from the matrix of Table 3, as read from left to right progressing from the top to the bottom row.
TABLE 3 ______________________________________ 0 0 0 0 2 .pi./3 4 .pi./3 0 4 .pi./3 8 .pi./3 ______________________________________
The phase in complex numbers is shown in Table 4.
TABLE 4 ______________________________________ 1 1 1 1 ##STR1## ##STR2## 1 ##STR3## ##STR4## ______________________________________
Each subsequence 12a-c represents a different frequency measured with respect to the carrier frequency, viz. 0, (2.pi.)/3.tau., and (4.pi.)/3.tau. (or -(2.pi.)/3.tau.) respectively for each of the subsequences in order.
It is known that the receivers of conventional radars are band-limited. That is to say, the gain of the receiver is inversely-proportional to the frequency deviation from the carrier frequency. Thus, a pulse, such as shown in FIG. 1b, having an even number of subpulse subsequences 11a-d of different frequencies measured with respect to the carrier frequency is attenuated unevenly across the pulse. The end subsequences for which the frequencies are closest to the carrier frequence are attenuated the least, while the center subsequences, for which the frequencies are furthest away from the carrier frequency, are attenuated the most. Specifically, the first, second and fourth subsequences 11a, 11b and 11d having respective frequencies of 0, (carrier frequency) (.pi./2)/.tau. and -(.pi./2)/.tau. are attenuated the least, while the third subsequence 11c having a frequency of .pi./.tau. is attenuated the most. A pulse, such as shown in FIG. 1d, having an odd number of subpulse sequences 12a-c of different frequencies measured with respect to the carrier frequency is also attenuated unevenly across the pulse. The end subsequence whose frequency is at the carrier frequency is attenuated the least while the center and opposite end subsequences whose frequencies are furthest away from the carrier frequency are attenuated the most. Specifically, the first subsequence having a frequency of 0 (carrier frequency) is attenuated the least, while the second and third subsequences having frequencies of (2.pi.)/3.tau. and -(2.pi.)/3.tau. are attenuated the most. This inverse weighting disadvantageously reduces the ratio between the correlation peak of the auto-correlation function and the level of the sidelobes. The latter is undesirable because it increases the possibility that weak target echos will be hidden by the sidelobes from an adjacent stronger target echo.